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AP EAMCET201923 Apr 2019Morning ShiftMathematicsMatricesActual

If (A ) is a (3 3 ) matrix and (|A|=2 ), then ( Adj ) (( Adj A) Adj ( Adj A)= )

Options

  1. A(32 ~A )
  2. B(64 ~A )
  3. C(16 ~A )
  4. D(8 ~A )

Correct answer

A. (32 ~A )

Step-by-step solution

As, adj ( adj ( A )=|A|^ n-2 A ), where (n ) is the order of matrix (A ). and (| adj adj (A)|=|A|^ (n-1)^2 ) So, (| adj adj A|( adj adj A)=|A|^ (n-1)^2 |A|^ n-2 A ) (=2^4 2 A=2^5 A=32 A . ) ([ |A|=2 and n=3] ) Hence, option (a) is correct.

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